The obligation to answer Amen to a Mi Shebeirach and to a blessing of a Jew:[1]

Whenever one hears someone blessing a Jew [or praying for a certain matter[2]], it is a Mitzvah[3] for the listeners to answer Amen to his blessing [or prayer[4]]. [This applies to all people who hear the blessing, even if the blessing was intended for a specific individual.] It is for this reason that we answer Amen to the Harachaman’s said in Birchas Hamazon by the leader of the Zimun.[5] [This applies even though Hashem’s name is not mentioned in the blessing.[6] Thus, all those who hear a Mi Shebeirach said in Shul, or a personal blessing given by a friend such as by a Farbrengen and the like, are to answer Amen to the blessing.[7] Another example of this would be for a mourner to answer Amen towards the comforters parting remarks of consolement.[8] One is however not to answer Amen to a blessing which is said without Hashem’s name due to doubt, such as the blessing of Baruch Patrani Meonsho Shel Zeh.[9] If a gentile gives a Jew a blessing, one is not to answer Amen to his blessing unless he does not mention G-d’s name in the blessing[10], or he is known to be monotheistic, such as a Muslim.[11] If he does not mention G-d’s name in the blessing, then one is to answer Amen.[12]]

May one answer Amen to a Mi Shebeirach if he is in middle of Davening?[13]

No. Starting from the blessing of Baruch Sheamar one may no longer answer Amen to a Mi Shebeirah and the like, even though one may answer Amen to a blessing which was instituted by the Sages.

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[1] Admur 189:6; M”A 215:3 in name of Midrash; Chesed Lealafim 215:4; Kaf Hachaim 187:4; 215:11

[2] M”A ibid

[3] Admur ibid

Is this a Mitzvah or obligation? Some Poskim rule that this answering of Amen is a mere Mitzvah and is not obligatory. [Implication of the wording of Admur ibid “Mitzvah” that it is not an obligation but a Mitzvah and Midas Chassidus to answer Amen and so is also implied from Orchos Chaim Kerias Hatorah 3 that says “It is permitted to answer Amen” and so rules Emek Sheila 53:2] However, some Poskim rule it is an see an obligation to answer Amen to a prayer or blessing, such as Harachaman. [M”A 215:3 in name of Midrash; Chesed Lealafim 215:4; Kaf Hachaim 215:11]

[4] M”A ibid; Chesed Lealafim 215:4; Kaf Hachaim 215:11

[5] Admur ibid; M”A 189:1; 215:3; Kol Bo 99 in name of Geonim

[6] M”A ibid

[7] See Aruch Hashulchan 215:1; Kaf Hachaim ibid; Piskeiy Teshuvos 215:7 footnote 42

[8] Piskeiy Teshuvos ibid

[9] Betzeil Hachochmah 5:90

[10] Kaf Hachaim 215:11

[11] See Admur 215:2

[12] Kaf Hachaim 215:11

[13] Piskeiy Teshuvos 51:11; See Admur 51:3 and 6